Struktura portfeli efektywnych w modelach średnia-wariancja-skośność
The Structure of Eficient Portfolios in Mean-variance-skewness Models

Summary/Abstract: Purpose – The distributions of rates of return observed in the investment practice are asymmetric, so the models which take into account only the mean and variance lack important features of portfolios. The aim of this paper is to analyse the degree of portfolio diversification, considering additional criterion of maximization of the third central moment as a measure of skewness. Design/Methodology/approach – In this paper we analyse the subsets of efficient portfolios which have the same structure. Using additional criterion of maximisation of the third central moment we determine the optimal portfolios having the same degree of diversification. In our research we analyse portfolios of stocks listed on Warsaw Stock Exchange. Findings – We show that consideration of skewness in the efficient portfolio analysis changes the structure of optimal portfolios significantly. The greater the strength of preferences for skewness the lower the degree of portfolio diversification. Originality/Value – We propose a three-criteria optimal portfolio selection model which maximises the expected value and skewness and minimises the variance. Parametric analysis of the level of diversification allows us to study the stability of the structure of optimal portfolios in relation to the investor preferences regarding the expected return and skewness.

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